Mesoscopic physics of swollen polymer networks: Statics and dynamics

We investigate in this paper the origin of the "butterfly" patterns that were discovered during small-angle-neutron-scattering studies of uniaxially stretched gels and rubbers and of polymer blends in extensional flow. We present a general formalism for both gels and liquids which shows that when material parameters such as shear modulus or viscosity are allowed to depend on the internal degrees of freedom (e.g., the monomer concentration), then butterfly patterns are naturally encountered in the isointensity contours of the structure factor. We also show that for higher strains (or strain rates for liquids), one encounters strain-induced decomposition. The dynamics of strain and of flow-induced decomposition are shown to be closely similar. To test the theoretical description, we compute the inelastic-light-scattering spectrum and the time evolution of the small-angle neutron-scattering cross section.